A cold drink initially at 40°F warms up to 44°F in 3 min while sitting in a room of temperature 70°F. How warm will the drink be if left out for 30 min?If the drink is left out for 30 min, it will be about(Round to the nearest tenth as needed.)°F.

Answered: A cold drink initially at 40°F warms up…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A cold drink initially at 40°F warms up to 44°F in 3 min while sitting in a room of temperature 70°F. How warm will the drink be if left out for 30 min?
If the drink is left out for 30 min, it will be about
(Round to the nearest tenth as needed.)
°F.

Expert Solution

Step 1

Introduction

Using the Netwons law of cooling, we will determine the drink's temperature in this problem if it is left for 30 minutes. Initially, considering the beginning condition, we will compute the temperature constant of Newton's law of cooling. Then, we will compute the temperature after 30 minutes.

Given data:

$\begin{array}{rcl} initial temperature of cold drink {(T)}_{1} & = & 40 ° F \\ final temperature of cold drink (T) & = & 44 ° F \\ time taken for the final temperature (t) & = & 3 \min \\ room temperature {(T)}_{R} & = & 70 ° F \end{array}$

Determine:

If the drink is left for 30 minutes, the temperature of the drink is.

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